Free Bioreactor 3D Simulator & Digital Twin | Microbial ODE Kinetics

ODE KINETICS & INITIAL SKID MONOD MODEL

Max Growth Rate μ_max (h⁻¹) 0.450 h⁻¹

Affinity Constant Ks (g/L) 0.150 g/L

Biomass Yield Y_X/S (g/g) 0.500 g/g

Initial Biomass X₀ (g/L) 0.20 g/L

Passed from Inoculum Workstation (Step 1)

Initial Substrate S₀ (g/L) 25.0 g/L

Mass Transfer kLa (h⁻¹) 120 h⁻¹

Passed from kLa Predictor (Step 4)

Run Duration (hours) 24.0 h

TIME-COURSE DYNAMICS SIMULATION TRAJECTORY NUMERICAL RK4 / EULER

Biomass X(t) [g/L]

Substrate S(t) [g/L]

Dissolved Oxygen DO(t) [%]

Product P(t) [g/L]

3D DIGITAL TWIN REACTOR SKID LIVE AGITATION

Bioprocess State

Agitation: 350 RPM
DO Status: 24.8% (Non-hypoxic)
Cell Density: 12.5 g/L (Optical Broth)

📊 Computed Results & Analytical Outputs LIVE CALCULATION

Peak Biomass (X_max)
12.5 g/L
From X₀ = 0.20 g/L inoculum

Glucose Depletion Time
11.2 h
S₀: 25.0 g/L consumed

        Minimum DO Sag
        Safe (>20%)
      
24.8 %
Occurred at peak growth (t ≈ 9.4 h)

Final Product Titer
1.88 g/L
Bioprocess Yield Y_P/S: 0.075 g/g

📚 Bioreactor 3D Simulation & Coupled ODE Kinetic Digital Twin Guide Upstream Bioprocess • Step 7 of 7

Theoretical Principles & Engineering Fundamentals

Modern biomanufacturing relies on physics-informed digital twins to simulate dynamic fermentation trajectories in silico. This simulator solves the coupled non-linear ordinary differential equations (ODEs) governing biomass growth ($X$), carbon consumption ($S$), dissolved oxygen ($DO$), product synthesis ($P$), and broth thermal balance ($T$) in real time using 4th-order Runge-Kutta numerical integration.

Governing Equations & Mathematical Formulations

Biomass Growth Rate (Monod) \frac{dX}{dt} = \mu_{\max} \frac{S}{K_s + S} X - D_v X

Coupled cell growth including dilution rate $D_v = F/V$.

Substrate Depletion Dynamics \frac{dS}{dt} = -\frac{1}{Y_{X/S}} \frac{dX}{dt} - m_s X + \frac{F}{V} (S_{\text{feed}} - S)

Substrate mass balance incorporating cell maintenance coefficient $m_s$.

Dissolved Oxygen Mass Balance \frac{dC_L}{dt} = k_L a (C^* - C_L) - q_{O_2} X

Dynamic balance between interfacial gas dissolution and metabolic consumption.

Industrial Benchmark Data & Parameter Reference

ODE State Variable	Units	Governing Phenomenon	Numerical Solver
Biomass (X)	g/L CDW	Monod microbial kinetics & cell division	Runge-Kutta 4th Order
Substrate (S)	g/L Glucose	Carbon consumption, yields & maintenance	Runge-Kutta 4th Order
Dissolved Oxygen (DO)	% Saturation	Mass transfer (kLa) vs respiratory demand	Adaptive Time-stepping
Product Titer (P)	g/L Titer	Luedeking-Piret mixed-growth synthesis	Runge-Kutta 4th Order

Frequently Asked Questions (Bioprocess Engineering FAQ)

How does the digital twin handle temperature and pH inhibition?

The simulation incorporates Arrhenius temperature deactivation and bell-shaped cardinal pH functions that dynamically suppress $\mu_{\max}$ when broth conditions drift outside optimal bounds.

Can this simulator predict foaming and antifoam addition?

Yes, hydrodynamic gas hold-up and protein secretion profiles trigger automated foam prediction routines that dynamically adjust effective liquid volume and $k_L a$.

How do I export simulated run data?

Click the 'Export CSV' button to download the entire simulated time-course dataset for offline modeling in Python, MATLAB, or JMP.

BioFlo Bioprocess Engineering Network

This calculator is maintained by the simulation engineers at BioFlo Bioprocess Engineering. We specialize in industrial bioreactor design, computational fluid dynamics (CFD) modeling, oxygen mass transfer optimization, and custom digital twin development for pharmaceutical fermentation plants.

🌐 BioFlo Corporate & CFD Simulation 🔬 Full Bioprocess Workbench (14 Free Tools) ◂ Previous: Fed-Batch Feeding Planner Next: 5L Bioreactor 3D Twin ▸ 🏭 Bioreactor Scale-Up 💨 kLa Mass Transfer 🧱 TFF Ultrafiltration